Closed Range Estimates for $$\bar{\partial }_b$$ on CR Manifolds of Hypersurface Type

On the regularity of CR mappings between CR manifolds of hypersurface type

We prove smooth and analytic versions of the classical Schwarz reflection principle for transversal CR mappings between two Levi-nondegenerate CR manifolds of hypersurface type.

Non-local Heat Flows and Gradient Estimates on Closed Manifolds

Abstract. In this paper, we study two kind of L norm preserved non-local heat flows on closed manifolds. We first study the global existence, stability and asymptotic behavior to such non-local heat flows. Next we give the gradient estimates of positive solutions to these heat flows. Mathematics Subject Classification (2000): 35J60, 53C21, 58J05

HÖLDER AND L ESTIMATES FOR b ON CR MANIFOLDS OF ARBITRARY CODIMENSION

The ∂̄b complex on the boundary of a complex manifold was first formulated by Kohn-Rossi [KR] to study the boundary values of holomorphic functions and holomorphic extensions. In this paper we study ∂̄b and b on a CR manifold of arbitrary codimension. When the CR manifold M is of codimension 1 and strongly pseudoconvex (or more generally, when M satisfies condition Y (q)), Kohn [K2] proved that b...

MAXIMAL L AND POINTWISE HÖLDER ESTIMATES FOR b ON CR MANIFOLDS OF CLASS C

A CR manifold, as first formulated in Kohn-Rossi [KR], is a smooth 2n + 1-dimensional real manifold equipped with an integrable CR structure. It was due to Kohn [K2] who first showed that the so-called Kohn’s Laplacian b on (p, q)-forms satisfies subelliptic estimates on any CR manifold whose Levi form satisfies condition Y (q). The results of Hölder and L estimates for b and the Szegö projecti...

Curvature of a Closed Hypersurface